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Cusp forms and finite subgroups in \(SL(5, \mathbb{C})\). (English. Russian original) Zbl 0847.11022

Funct. Anal. Appl. 29, No. 2, 129-130 (1995); translation from Funkts. Anal. Prilozh. 29, No. 2, 71-73 (1995).
This is an announcement of results concerning the following problem: Find a finite group such that all 28 multiplicative eta-products can be associated with elements of this group by means of some representation. It is known [G. Mason, Math. Ann. 283, 381-409 (1989; Zbl 0636.10021)] that 21 of these eta-products are associated with the Mathieu group \(M_{24}\). The author claims that all multiplicative eta-products with weight \(> 1\) can be associated with finite order elements of \(\text{SL}(5, \mathbb{C})\).

MSC:

11F20 Dedekind eta function, Dedekind sums
11F11 Holomorphic modular forms of integral weight
11F22 Relationship to Lie algebras and finite simple groups

Citations:

Zbl 0636.10021
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Full Text: DOI

References:

[1] G. Mason, Contemp. Math.,45, 223-244 (1985).
[2] G. Mason, Math. Ann.,283, 381-409 (1989). · Zbl 0636.10021
[3] D. Dummit, H. Kisilevsky, and J. McKay, Contemp. Math.,45, 89-98 (1985).
[4] M. Koike, Nagoya Math. J.,95, 85-89 (1984).
[5] G. V. Voskresenskaya, Mat. Zametki,52, No. 1, 25-31 (1992).
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